Elements of Geometry...: Translated from the French for the Use of the Students of the University at Cambridge, New England |
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Page x
... ratio , it is evi- dent that the two other ratios may be put into a proportion , since they are each equal to that which is common . If , for ex- ample , we have then we shall have A : B : CD , X Introduction .
... ratio , it is evi- dent that the two other ratios may be put into a proportion , since they are each equal to that which is common . If , for ex- ample , we have then we shall have A : B : CD , X Introduction .
Page xi
... ratio then will be equal to the primitive ratio increased by unity . If the same operation be performed upon the two ratios of a proportion , there will evidently result from it two new ratios equal to each other , and consequently a ...
... ratio then will be equal to the primitive ratio increased by unity . If the same operation be performed upon the two ratios of a proportion , there will evidently result from it two new ratios equal to each other , and consequently a ...
Page xii
... ratios A : C , B : D , being common to the two proportions above obtained , it follows that the other ratios of the same proportions are equal , and that consequently B + A : D + C :: B - A : D - C , or , by changing the place of the ...
... ratios A : C , B : D , being common to the two proportions above obtained , it follows that the other ratios of the same proportions are equal , and that consequently B + A : D + C :: B - A : D - C , or , by changing the place of the ...
Page xiii
... ratios A : BC : :: C : D :: E : F , by considering only the two first , which form the proportion A : B :: C : D , we obtain by what precedes A + C : B + D :: A : B ; and , since the third ratio E : F , is equal to the first A : B , we ...
... ratios A : BC : :: C : D :: E : F , by considering only the two first , which form the proportion A : B :: C : D , we obtain by what precedes A + C : B + D :: A : B ; and , since the third ratio E : F , is equal to the first A : B , we ...
Page xiv
... ratios B F D H and and A E C G ' which are equal . by If we multiply the proportion we shall have ( II ) A : B :: C : D A : B :: C. D A2 : B2 : C2 : D2 , whence it follows , that the squares of four proportional quantities form a new ...
... ratios B F D H and and A E C G ' which are equal . by If we multiply the proportion we shall have ( II ) A : B :: C : D A : B :: C. D A2 : B2 : C2 : D2 , whence it follows , that the squares of four proportional quantities form a new ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circle circular sector circumference circumscribed common cone consequently construction convex surface Corollary cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent figure formed four right angles frustum Geom given point gles greater hence homologous sides hypothenuse hypothesis inclination inscribed isosceles join less let fall line AC measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN point F polyedron prism proposition quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium sector segment semicircumference side AC sides AB similar solid angle sphere spherical polygons spherical triangle straight line tangent THEOREM third side triangle ABC triangles are equal triangular prism triangular pyramids vertex vertices whence
Popular passages
Page 43 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 3 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 4 - Hence a straight line drawn from the vertex of an isosceles triangle, to the middle of the base, is perpendicular to that base, and divides the vertical angle into two equal parts.
Page 16 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 58 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 158 - CD, &c., taken together, make up the perimeter of the prism's base : hence the sum of these rectangles, or the convex surface of the prism, is equal to the perimeter of its base multiplied by its altitude.
Page 32 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Page 142 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Page 136 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle; produce the sides AB, AU, till they meet again in D.
Page 154 - ABCDE, and equal in altitude to the cylinder, is said to be inscribed in the cylinder, or the cylinder to be circumscribed about the prism.